Okay, here's some information about f(2x)
in Markdown format, with links to placeholder URLs.
# Understanding f(2x)
The expression `f(2x)` represents a transformation of the function `f(x)`. Specifically, it demonstrates a **[horizontal compression](https://www.wikiwhat.page/kavramlar/Horizontal%20Compression)** by a factor of 1/2.
## Key Concepts:
* **[Function Transformation](https://www.wikiwhat.page/kavramlar/Function%20Transformation)**: This is the general concept of altering the graph of a function using various operations. `f(2x)` falls under this umbrella.
* **[Horizontal Scaling](https://www.wikiwhat.page/kavramlar/Horizontal%20Scaling)**: `f(2x)` scales the x-values. Because the input to the function is now `2x` instead of `x`, the function behaves as if the x-axis has been squeezed inward.
## How it Works:
To obtain the graph of `y = f(2x)` from the graph of `y = f(x)`, you effectively halve the x-coordinate of every point on the original graph. For example:
* If `f(4) = 5`, then to get the same output of 5, we need `f(2x) = f(2*2) = f(4) = 5`. This means the point (4,5) on f(x) becomes (2,5) on f(2x).
* In general, the point `(x, y)` on the graph of `y = f(x)` corresponds to the point `(x/2, y)` on the graph of `y = f(2x)`.
## Example:
If `f(x)` is a **[parabola](https://www.wikiwhat.page/kavramlar/Parabola)** with a vertex at (2, 0), then `f(2x)` would be a parabola with a vertex at (1, 0). The parabola is compressed horizontally.
## Important Note:
The factor by which the x-coordinate is changed is the *reciprocal* of the number multiplying `x` inside the function. So, in `f(2x)`, we compress by a factor of 1/2. If it was `f(x/2)`, we would stretch horizontally by a factor of 2.
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